%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWW430-1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:07:50 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.67s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 117
% Number of leaves : 11
% Syntax : Number of formulae : 149 ( 68 unt; 5 def)
% Number of atoms : 287 ( 32 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 266 ( 128 ~; 133 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 19 ( 4 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [S,T,Sigma] : sep(S,sep(T,Sigma)) = sep(T,sep(S,Sigma)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Sigma] : sep(lseg(X,X),Sigma) = Sigma,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z,Sigma] :
( X = Z
| X = Y
| ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
x3 != x11,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
x3 != x12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
heap(sep(lseg(x5,x2),sep(lseg(x5,x7),sep(lseg(x5,x4),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1,X2] : sep(X0,sep(X1,X2)) = sep(X1,sep(X0,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1] : sep(lseg(X0,X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X,Z] :
( X = Z
| ! [Y] :
( X = Y
| ! [Sigma] : ~ heap(sep(lseg(X,Y),sep(lseg(X,Z),Sigma))) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| X0 = X1
| ~ heap(sep(lseg(X0,X1),sep(lseg(X0,X2),X3))) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f37,plain,
x3 != x11,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
x3 != x12,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f42,plain,
heap(sep(lseg(x5,x2),sep(lseg(x5,x7),sep(lseg(x5,x4),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f51,plain,
heap(sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f42]) ).
fof(f52,plain,
heap(sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x12,x1),sep(lseg(x5,x4),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f51]) ).
fof(f53,plain,
heap(sep(lseg(x5,x7),sep(lseg(x12,x1),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f52]) ).
fof(f54,plain,
heap(sep(lseg(x12,x1),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f53]) ).
fof(f55,plain,
heap(sep(lseg(x12,x1),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x12,x6),sep(lseg(x5,x4),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f54]) ).
fof(f56,plain,
heap(sep(lseg(x12,x1),sep(lseg(x5,x7),sep(lseg(x12,x6),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f55]) ).
fof(f57,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x2,x12),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f56]) ).
fof(f58,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x2,x12),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f57]) ).
fof(f59,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x5,x7),sep(lseg(x2,x12),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f58]) ).
fof(f60,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f59]) ).
fof(f61,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x3,x11),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f60]) ).
fof(f62,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x3,x11),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f61]) ).
fof(f63,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x3,x11),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f62]) ).
fof(f64,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x3,x11),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f63]) ).
fof(f65,plain,
heap(sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x3,x11),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f64]) ).
fof(f66,plain,
heap(sep(lseg(x12,x1),sep(lseg(x3,x11),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f65]) ).
fof(f67,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f66]) ).
fof(f68,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x3,x1),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f67]) ).
fof(f69,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x3,x1),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f68]) ).
fof(f70,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x3,x1),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f69]) ).
fof(f71,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x3,x1),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f70]) ).
fof(f72,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x3,x1),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f71]) ).
fof(f73,plain,
heap(sep(lseg(x3,x11),sep(lseg(x12,x1),sep(lseg(x3,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f72]) ).
fof(f74,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x3,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f73]) ).
fof(f75,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x3,x6),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f74]) ).
fof(f76,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x3,x6),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f75]) ).
fof(f77,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x3,x6),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f76]) ).
fof(f78,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x3,x6),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f77]) ).
fof(f79,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x3,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f78]) ).
fof(f80,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x12,x1),sep(lseg(x3,x6),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f79]) ).
fof(f81,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x9,x10),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f80]) ).
fof(f82,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x9,x10),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f81]) ).
fof(f83,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f82]) ).
fof(f84,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f83]) ).
fof(f85,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x11,x8),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f84]) ).
fof(f86,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x11,x8),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f85]) ).
fof(f87,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x11,x8),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f86]) ).
fof(f88,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x11,x8),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f87]) ).
fof(f89,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x11,x8),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f88]) ).
fof(f90,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x11,x8),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f89]) ).
fof(f91,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x12,x1),sep(lseg(x11,x8),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f90]) ).
fof(f92,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x11,x6),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f91]) ).
fof(f93,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x11,x6),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f92]) ).
fof(f94,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x11,x6),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f93]) ).
fof(f95,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x11,x6),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f94]) ).
fof(f96,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x11,x6),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f95]) ).
fof(f97,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x11,x6),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f96]) ).
fof(f98,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x11,x6),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f97]) ).
fof(f99,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x11,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f98]) ).
fof(f100,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x11,x6),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f99]) ).
fof(f101,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x8),sep(lseg(x11,x6),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f100]) ).
fof(f102,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f101]) ).
fof(f103,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x9,x10),sep(lseg(x1,x8),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f102]) ).
fof(f104,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x9,x10),sep(lseg(x6,x2),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f103]) ).
fof(f105,plain,
heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x1,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp)))))))))))))))))),
inference(forward_demodulation,[status(thm)],[f19,f104]) ).
fof(f106,plain,
( x3 = x1
| x3 = x11 ),
inference(resolution,[status(thm)],[f105,f28]) ).
fof(f107,definition,
( sQ2_spl
<=> x3 = x11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ2_spl
| x3 = x11 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,definition,
( sQ3_spl
<=> x3 = x1 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ3_spl
| x3 = x1 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f106,f107,f110]) ).
fof(f114,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f37]) ).
fof(f115,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x1),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x3,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp)))))))))))))))))) ),
inference(backward_demodulation,[status(thm)],[f111,f105]) ).
fof(f117,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x3),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x3,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp)))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f111,f116]) ).
fof(f118,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x3),sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x3,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp)))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f117]) ).
fof(f119,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x1),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x3,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f20,f118]) ).
fof(f120,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x3,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f111,f119]) ).
fof(f121,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f120]) ).
fof(f122,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x3,x8),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f121]) ).
fof(f123,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x3,x8),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f122]) ).
fof(f124,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x3,x8),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f123]) ).
fof(f125,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x3,x8),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f124]) ).
fof(f126,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x3,x8),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f125]) ).
fof(f127,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x3,x8),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f126]) ).
fof(f128,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x3,x8),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f127]) ).
fof(f129,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x3,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f128]) ).
fof(f130,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x11,x6),sep(lseg(x3,x8),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f129]) ).
fof(f131,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x1,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f130]) ).
fof(f132,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x9),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f111,f131]) ).
fof(f133,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x3,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f132]) ).
fof(f134,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x3,x9),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f133]) ).
fof(f135,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x3,x9),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f134]) ).
fof(f136,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x3,x9),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f135]) ).
fof(f137,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x3,x9),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f136]) ).
fof(f138,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x3,x9),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f137]) ).
fof(f139,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x3,x9),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f138]) ).
fof(f140,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x3,x9),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f139]) ).
fof(f141,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x3,x9),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f140]) ).
fof(f142,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x8),sep(lseg(x3,x9),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f141]) ).
fof(f143,plain,
( ~ sQ3_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x6,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f142]) ).
fof(f144,plain,
( ~ sQ3_spl
| x3 = x6
| x3 = x11 ),
inference(resolution,[status(thm)],[f143,f28]) ).
fof(f145,definition,
( sQ4_spl
<=> x3 = x6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| x3 = x6 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( ~ sQ3_spl
| sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f144,f107,f145,f110]) ).
fof(f149,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x6),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(backward_demodulation,[status(thm)],[f146,f143]) ).
fof(f150,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x3),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f146,f149]) ).
fof(f151,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x3),sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x2),sep(lseg(x9,x10),emp))))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f150]) ).
fof(f152,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x6),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x2),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f20,f151]) ).
fof(f153,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x6),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x2),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f146,f152]) ).
fof(f154,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x3,x2),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f146,f153]) ).
fof(f155,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x3,x2),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f154]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x3,x2),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f155]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x3,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f156]) ).
fof(f158,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x3,x2),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f157]) ).
fof(f159,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x3,x2),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f158]) ).
fof(f160,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x3,x2),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f159]) ).
fof(f161,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x3,x2),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f160]) ).
fof(f162,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x3,x2),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f161]) ).
fof(f163,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x3,x2),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f162]) ).
fof(f164,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x3,x2),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f163]) ).
fof(f165,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x2),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f164]) ).
fof(f166,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x2),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x2),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f165]) ).
fof(f167,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| x3 = x2
| x3 = x11 ),
inference(resolution,[status(thm)],[f166,f28]) ).
fof(f168,definition,
( sQ5_spl
<=> x3 = x2 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ5_spl
| x3 = x2 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ5_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f167,f107,f168,f145,f110]) ).
fof(f172,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x2),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(backward_demodulation,[status(thm)],[f169,f166]) ).
fof(f175,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x3),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f169,f172]) ).
fof(f176,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x3),sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp)))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f175]) ).
fof(f177,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x2,x12),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f20,f176]) ).
fof(f178,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x3,x12),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f169,f177]) ).
fof(f179,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x3,x12),sep(lseg(x12,x3),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f178]) ).
fof(f180,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x3,x12),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f179]) ).
fof(f181,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x3,x12),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f180]) ).
fof(f182,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x3,x12),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f181]) ).
fof(f183,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x9),sep(lseg(x3,x12),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f182]) ).
fof(f184,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x12),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x5,x7),sep(lseg(x5,x3),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f183]) ).
fof(f185,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| heap(sep(lseg(x3,x11),sep(lseg(x3,x12),sep(lseg(x3,x9),sep(lseg(x3,x8),sep(lseg(x11,x3),sep(lseg(x11,x8),sep(lseg(x12,x3),sep(lseg(x12,x3),sep(lseg(x5,x3),sep(lseg(x5,x7),sep(lseg(x5,x4),sep(lseg(x4,x9),sep(lseg(x4,x8),sep(lseg(x9,x10),emp))))))))))))))) ),
inference(forward_demodulation,[status(thm)],[f19,f184]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| x3 = x12
| x3 = x11 ),
inference(resolution,[status(thm)],[f185,f28]) ).
fof(f187,definition,
( sQ6_spl
<=> x3 = x12 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ6_spl
| x3 = x12 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f186,f107,f187,f168,f145,f110]) ).
fof(f191,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f38]) ).
fof(f192,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f193,plain,
$false,
inference(sat_refutation,[status(thm)],[f113,f115,f148,f171,f190,f192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW430-1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n002.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 09:54:50 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.59 % Drodi V4.1.1
% 0.14/0.67 % Refutation found
% 0.14/0.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.69 % Elapsed time: 0.108533 seconds
% 0.14/0.69 % CPU time: 0.584704 seconds
% 0.14/0.69 % Total memory used: 112.743 MB
% 0.14/0.69 % Net memory used: 112.056 MB
%------------------------------------------------------------------------------